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Question
Write the minor and cofactor of element of the first column of the following matrix and hence evaluate the determinant:
\[A = \begin{bmatrix}5 & 20 \\ 0 & - 1\end{bmatrix}\]
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Solution
\[M_{11} = - 1\]
\[ M_{21} = 20\]
\[ C_{ij} = \left( - 1 \right)^{i + j} M_{ij} \]
\[ C_{11} = \left( - 1 \right)^{1 + 1} \left( - 1 \right) = - 1\]
\[ C_{21 =} \left( - 1 \right)^{1 + 2} \left( 20 \right) = - 20\]
\[D = \left( - 1 \times 5 \right) - \left( 20 \times 0 \right) = - 5\]
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